Answer-first summary for fast verification
Answer: Ten (10)
The optimal hedge ratio is: \[ h^* = \rho \times \frac{\sigma_S}{\sigma_F} \] Substituting the values: \[ h^* = 0.850 \times \frac{200}{340} = 0.50 \] Then the number of futures contracts to short is: \[ N^* = h^* \times \frac{Q_A}{Q_F} \] where: - \(Q_A = 100\) BTC to be hedged - \(Q_F = 5\) BTC per futures contract So: \[ N^* = 0.50 \times \frac{100}{5} = 10 \] Therefore, the trader should short **10 contracts**.
Author: Manit Arora
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Question 21.13.3. The daily standard deviation of Bitcoin (BTC) is $200.00, while the standard deviation of the futures contract price (on the same BTC) is $340.00. The correlation between the two changes is 0.850. If the size of one futures contract is five Bitcoins (5 BTC), and the trader seeks to hedge the purchase of 100 Bitcoins (100 BTC), then how many contracts should be shorted to hedge?
A
One (1)
B
Three (3)
C
Ten (10)
D
Twenty-five (25)
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